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STATS CHEAT SHEET
How do I decide which test to use?
What type of data do I have?
Continuous Data Only Categorical/Nominal data and Continuous data
Do I know the population and ?
Yes
Run a Z - Test
No
No
Do I know the population ?
Yes
Run a Single
Sample T-test
St. Dev. to predict
Run Correlation and/
or Regression
analysis
Do I have Independent Samples/Conditions?
Yes No
Run a Paired Samples
T-Test
Test-Retest
Do I have 2 conditions
or More conditions?
2 Conditons
Run an Independent Samples T-Test
- Look for experimental groups
- Clues: Unequal N’s or Random
Assignment to one or other group
3 or more Conditions
Run an ANOVA
- Look for experimental groups
- Clues: Unequal N’s or Random
Assignment to one or other group
Nominal (Frequency) Data
Run a Chi Square
Z-TESTS
In order to run a Z-Test you must be provided with
- Population
- Population
Equation:
N
Z X
/
Critical Z-Test values:
1-Tailed 2-Tailed
α = .05 1.64 1.96/-1.
α = .01 2.33 2.58/-2.
PAIRED SAMPLES T-TEST
Paired Samples T-Tests:
- Are also known as Dependent or Matched T-Tests
- Do not utilize population parameters, rather are a comparison of scores from a single
sample measured across time
- Look for key words such as “Test-retest”; “Pre-Post”; “Same individuals tested”
Equations:
S N
t D
D
/
1
/
2 2
N
D D N
S
D df = N - 1
Confidence Intervals: D t S N
crit D
INDEPENDENT SAMPLES T-TEST
(N’s Equal)
Independent Samples T-Tests:
- Are used to compare 2 Independent groups
- Have experimental groups / conditions
- May have unequal N’s
- Look for key words such as “Experiment”; “Conditions”; “Random Assignment to
one condition or another”
Equations:
2
2
2
1
2
1
1 2
( )
n
S
n
S
t X X
2 2 2
N
S x x N
N = n 1
df = N - 2
Confidence Intervals:
2
2
2
1
2
1
1 2
n
S
n
S
X X t
crit
ANOVA
AN alysis O f VA rience:
- Are virtually the same thing as an Independent T-Test except that there are more than
2 conditions
- Accounts for possible inflation of the level by dividing the level between all
possible comparisons (i.e. 3 conditions = /3 .: of 0.017 per comparison)
Equations:
Source
Sums of Squares
(SS)
df
Mean Square Error
(MS)
F
Between =
N
X
n
X
tot
k
i
i
2
1 1
2
k-1 =
Btwn
Btwn
df
SS
Within
Btwn
MS
MS
Within SS
Tot
- SS
Btwn
N-k
Within
Within
df
SS
OR
N
n S
i i
2
Total =
N
X X
tot tot
2 2
N-
Estimating the Magnitude of Experimental Effect:
(eta) =
TOT
TOT WITHIN
SS
SS SS
2
(omega) =
TOT WITHIN
BTWN WITHIN
SS MS
SS k MS
2
CHI SQUARE
Chi Square:
Is used when you have ordinal data
You are using the obtained data to make a prediction about what the relationship
would have been if there were no difference between the groups
Equations:
E
O E
2
2
( )
N
R C
E
i j
ij
df ( R 1 )( C 1 )
Likelihood Ratio:
ij
ij
R C ij
E
O
2 O ln
2
( 1 )( 1 )
Measures of Association:
Used to test the strength of the relationship
Phi: (2 by 2)
N
2
Cramér’s Phi: (X by X)
( 1 )
2
N k
C
Odd’s Ratio: (2 by 2)
j
i
C
R
P
POWER
Power Calculations:
What is the probability of correctly rejecting a false H
0
Power is a function of:
o
level
o
H
1
o
Sample size
o
Test statistic used
Where n is unknown, used the power table to estimate on a given level.
Power for 1 sample
Effect Size Noncentrality parameter Estimating Required Sample Size
1 0
d d n
2
d
n
Power for 2 samples (N’s Equal)
Effect Size Noncentrality parameter Estimating Required Sample Size
1 0
d
2
n
d
2
2
d
n
Power for 2 samples (N’s Unequal)
Effect Size
*Where is pooled
Harmonic N Noncentrality parameter Estimating Required Sample Size
1 0
d
1 2
1 2
n n
n n
n h
2
n h
d
2
2
d
n
Power when is known
Effect Size Noncentrality parameter Estimating Required Sample Size
1
d 1
1
N
1
2
1
n
